They were, like the modern Republicans, an uneasy coalition of pro-business individuals on the one hand and religious revivalists on the other. Then, as now, the division was geographical and social: Northern business interests on the one hand and the Southern, pro-slavery group on the other. Meanwhile, two of its most influential leaders--Henry Clay and Daniel Webster--both died, leaving a void that, in the end, no one could effectively fill. (Clay had served as senator, secretary of state and Speaker of the House; Webster had served in the Senate and also as secretary of state.) With the compromise of 1850, the party split along pro- and anti-slavery lines and was, like Humpty Dumpty, irreparably broken.
If this sounds familiar, it should. Today's Republican Party finds itself divided between a pro-business faction on the one hand and religious revivalists on the other. The latter faction finds most of its strength in the South and, to some extent, the Midwest. It's also dominated by white males. As in the 1850s, the party is bogged down by social issues, in this case contraception, same-sex marriage, military service for women and gays, etc. There's nothing like the overarching issue of slavery, which was an economic as well as a social consideration. Nevertheless, the passions associated with these modern issues are rising and may soon approach those once associated with slavery.
Moreover, the Republican Party leadership--like the Whig Party leadership a century and a half ago--is in shambles. The ideologues are busy rummaging through trash cans in a vain search for purists, attacking anyone who deviates a centimeter from their agenda and extracting absolute pledges from candidates that fall just short of swearing on their mothers' graves. The party's leaders? Apart from Romney, they're a motley crew who would have been benchwarmers (or batboys) for the party in its heydey: Gingrich is a disgraced former House Speaker, Santorum suffered the most humiliating defeat ever by a Republican senator, and Paul is a refugee from another party.
It also signals that the GOP won't take pollution, the environment, or science seriously. "Tommy the Two-Headed Trout proves all that bio-geno-stuff is a fraud," said one fanatic. "God can create a new animal whenever he wants to."
For more on conservatives, see Santorum Blind to America's Sins and Republicans Want to "Keep America America."